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A256670
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Decimal expansion of Integral_{x=0..1} x*exp(x^3) dx.
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0
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7, 8, 1, 1, 9, 7, 0, 3, 1, 1, 0, 8, 6, 5, 5, 9, 1, 5, 1, 0, 7, 4, 3, 2, 8, 1, 4, 3, 4, 8, 2, 9, 9, 5, 0, 5, 7, 7, 6, 6, 9, 7, 3, 9, 0, 9, 6, 2, 1, 7, 8, 6, 0, 3, 9, 8, 0, 9, 2, 6, 0, 2, 6, 8, 4, 3, 2, 4, 2, 3, 4, 0, 8, 2, 2, 1, 7, 0, 4, 5, 9, 3, 2, 9, 0, 2, 4, 2, 9, 3, 5, 3, 9, 1, 5, 8, 7, 3, 3, 7, 9, 1, 3
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OFFSET
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0,1
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REFERENCES
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Jonathan M. Borwein, Matthew P. Skerritt, An Introduction to Modern Mathematical Computing, Springer Science & Business Media, 2011, p. 89.
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LINKS
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FORMULA
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Equals (1/6)*(1 + i*sqrt(3))*(Gamma(2/3, -1) - Gamma(2/3)).
The simpler similar integral Integral_{x=0..1} x*exp(x^2) dx equals (e-1)/2 = 0.85914...
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EXAMPLE
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0.7811970311086559151074328143482995057766973909621786...
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MATHEMATICA
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int3 = (1/6)*(1 + I*Sqrt[3])*( Gamma[2/3, -1] - Gamma[2/3]); RealDigits[N[int3, 103] // Chop] // First
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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